What shapes can I sculpt with?
You can use any shape you want.
Sculpting modifies a mesh in real time, so at any point you can switch to edit mode and edit the polygons directly, then switch back to sculpt mode, etc.
There are two usual workflows for sculpting:
Dynamic topology
You don't need to subdivide your mesh if you use dynamic topology, the mesh will be dynamically subdivided as you sculpt.
Enable it in 3D view &gt; tool shelf &gt; Dyntopo (Topology pre 2.71), or by pressing CtrlD:

See the wiki for more info.
This will create a mesh of triangles, so depending on the project you may need to do retopology after you are finished sculpting.
Multiresolution
Non-destructively subdivide your mesh with a multi resolution modifier, which lets you handle multiple levels of subdivision at once.
Because of this, it's quite useful to use on a low poly model, sculpt details, and bake normals.
Also see What is the difference between a subdivision surface modifier and multiresolution modifier?